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I make naive, visual exploration of 2D images, which can be described by simple functions, like:

  1. $ y = f(x)$
  2. $ y = f(x,y)$
  3. $f(z) = \begin{cases} k(x,y) \\ h(x,y) \end{cases}$

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I have read about algebraic and differential equations.

These images are used in :

Questions:

Is there some math theory behind such images/functions/transformations ?

What is the difference between above functions?

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